Powell laid down the proposed six-month timetable last week amid mounting international pressure for a handover of power in Iraq. Powell said the United States will not relinquish power until a democratically elected Iraqi government is in place.
"We all want to see a constitution as soon as possible," said Entifadh Qanbar, spokesman for the current council president, Ahmad Chalabi.
He said it would take time for Iraqis to "coalesce" on issues regarding the framework of a new democratic Iraq. Then, he said, there had to be "adequate time" for the Iraqi people to discuss and understand any proposed constitution before holding a referendum on it.
"I don't think six months will be sufficient, but we must wait and see," he said. "This is up to the constitutional committee and the events. A lot of times deadlines do not necessarily stay as is, and reality drive what's happening."
In other developments:
A 25-member committee has been discussing how to draft a new constitution for weeks. However, major issues such as the role of Islam and power relationships among the major ethnic and culture groups have complicated the discussions.
With France leading pressure for a speedy handover of power, Washington has insisted it does not want to be too hasty in the transfer since the country still faces manifold problems as it recovers from years of war, dictatorship and economic ruin.
Meanwhile, an explosive thrown or fired from a passing car slightly injured an American soldier Tuesday on a bridge in northern Baghdad, witnesses said. U.S. troops killed an Iraqi resistance fighter and wounded four others in a separate attack north of the capital.
Elsewhere, one soldier drowned and another was missing after a vehicle overturned in a canal Monday night as troops were responding to a reported mortar attack near the Abu Ghraib prison on the western edge of Baghdad, the U.S. Central Command said.
Witnesses said the explosive that injured the American appeared to have been thrown or shot from a passing vehicle on a bridge over the Beirut Square traffic circle in the city's Nile neighborhood. It was the first such attack reported in the quiet residential and commercial neighborhood.
U.S. authorities on Tuesday relaxed a nighttime curfew in Baghdad, citing improvements in security and a recent reduction in crime. The military said that effective immediately, the curfew would run from midnight until 4 a.m. Previously, the curfew had begun at 11 p.m.
In Samara, 60 miles north of Baghdad, resistance fighters fired two rocket-propelled grenades at an American patrol late Monday but missed, U.S. officials reported.
The Americans returned fire, killing one assailant and wounding four others. The soldiers tracked the assailants into a nearby house, where 11 people were arrested and two rifles and one grenade were seized, according to Maj. Josslyn Aberle, spokeswoman of the 4th Infantry Division.
The soldier who drowned in the western Baghdad accident was from the 800th Military Police Brigade, a Central Command statement said. Two others who were in the vehicle swam to safety. A dive team soldier from the 82nd Airborne Division failed to resurface during the rescue attempt and is missing, the statement said.
Elsewhere, a homemade bomb exploded early Tuesday at the governor's office in Saddam Hussein's hometown of Tikrit, but no one was injured, U.S. officials reported. Two people were arrested for allegedly planting the device.